It is not as if Mbappe is not lured by money, of course money plays an important role in how footballers make decisions regarding their career. Mbappe was never going to move to Saudi Arabia because he is very young and one of the best players in the world, he is also already one of the highest paid footballers in the world in PSG and he also earns a huge amount in loyalty bonuses.
Liverpool can't even afford to pay Mbappe's wages for one year, thus there is no chance in hell that he is going to Anfield, Mbappe is either staying in PSG or moving to Real Madrid, i don't think there are any other feasible options.
I also don't expect Kylian Mbappe to move to the Arab Pro League when his career is as good as it is now. Liverpool have the possibility of getting Mbappe's services, but the chances are very low if we look at how Liverpool pay the salaries of their players. Liverpool and PSG might be able to come to an agreement like the wages are shared, but I think that's too bad for PSG.
PSG don't have many options in Mbappe's situation, if they can't extend Mbappe's contract then they have to sell him, loan him, or release him to another team on a free transfer at the end of next season. At the moment several approaches are possible, so as long as it will benefit PSG then they will probably find a deal.